1)Mandy is x years oldHer brother is 5 years older than MandyThe product of their ages is 84

Show that x^2 + 5x - 84 = 0

(^2 meaning x "squared")

Just factor the quadratic. See what two factors of 84 add to 5. After a few tries, you should come up with 7 and 12. So,

Mandy must be 7 years old and her brother is 5 years older making him 12.

You can't use the second solution of x = 12 because if Mandy were 12, then her brother would be 17 and the product of their ages would be 204. We call this an extraneous solution. It solves the quadratic, but doesn't make sense in the application.

Originally Posted by jinz

2)Solve the simultaneous equations

y=x+2y=3x^2 (^2 meaning x "squared")

you must show your working outDo not use a trial and improvement method.

Thanks any help would be appreciated!

Substitute y=x+2 into the second equation and solve for x.

Factor and find x. Then substitute each of these values into the original equations to find the corresponding value for y.

1)Mandy is x years old
Her brother is 5 years older than Mandy
The product of their ages is 84

Show that x^2 + 5x - 84 = 0

(^2 meaning x "squared")

do you know what "product" means? you need to learn your math vocabulary. you should know what words like "sum", "difference", "product", "percent", "of", "is" etc means.

"product" means to multiply.

so Mandy's age is x, and her bro's age is x + 5

what is the product of their ages? what is it equal to.

2)Solve the simultaneous equations

y=x+2
y=3x^2 (^2 meaning x "squared")

you must show your working out
Do not use a trial and improvement method.

Thanks any help would be appreciated!

you can replace y with x + 2 in the second equation, solve for x and then you can solve for y

Originally Posted by jinz

Could some please help me i need this for wednesday, P.S sorry for the double post, Im new!

Also,for question 2 do you have to draw a graph?

drawing graphs is a very inefficient method for solving simultaneous equations. especially if you are not just graphing straight lines. but if it's required, then simply use a graphing sheet to draw the graphs. their point(s) or intersection are the solutions. (the x-coordinate gives you the x-value and the y-coordinate gives you the y-value)